Self-avoiding paths on the pre-Sierpinski gasket

Kumiko Hattori, Tetsuya Hattori, Shigeo Kusuoka

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

We study a statistical mechanics of self-avoiding paths on the pre-Sierpinski gasket. We first show the existence of the thermodynamic limit of the (appropriately scaled) free energy. Then we show that there are two domains in the weight parameters (i.e. two phases) between which the scaling differs; i.e. there is a certain kind of phase transition in our model, and we find the critical exponents of the free energy at the phase transition point. We also show the convergence of the distribution of the scaled length of the paths at thermodynamic limit.

Original languageEnglish
Pages (from-to)1-26
Number of pages26
JournalProbability Theory and Related Fields
Volume84
Issue number1
DOIs
Publication statusPublished - 1990 Mar
Externally publishedYes

Fingerprint

Sierpinski Gasket
Thermodynamic Limit
Free Energy
Phase Transition
Path
Statistical Mechanics
Critical Exponents
Scaling
Thermodynamics
Phase transition
Energy
Model
Statistical mechanics

ASJC Scopus subject areas

  • Statistics and Probability
  • Analysis
  • Mathematics(all)

Cite this

Self-avoiding paths on the pre-Sierpinski gasket. / Hattori, Kumiko; Hattori, Tetsuya; Kusuoka, Shigeo.

In: Probability Theory and Related Fields, Vol. 84, No. 1, 03.1990, p. 1-26.

Research output: Contribution to journalArticle

Hattori, Kumiko ; Hattori, Tetsuya ; Kusuoka, Shigeo. / Self-avoiding paths on the pre-Sierpinski gasket. In: Probability Theory and Related Fields. 1990 ; Vol. 84, No. 1. pp. 1-26.
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